In abstract interpretation, approximation is encoded by abstract domains. Abstract domains provide a systematic guideline for defining abstract semantic functions as so-called best correct approximations of concrete semantic functions. However, it may happen that an abstract domain is unnecessarily too accurate for the specific purpose of approximating a given set of semantic functions. This work puts forward Abstraction-Guided Abstraction Simplification (AGAS), a methodology that allows to simplify abstract domains, i.e. to remove abstract values from them, in a maximal way while retaining exactly the same best correct approximations of concrete semantic functions. We show how AGAS can be applied in the context of abstract model checking by providing a simplification paradigm of abstract state spaces that can be viewed as a dual methodology to CounterExample-Guided Abstraction Refinement (CEGAR).